The present invention relates to a method of manufacturing a gradient coil, a gradient coil unit, a gradient coil and an MRI (magnetic resonance imaging) apparatus, and more particularly to a method of manufacturing a gradient coil, a gradient coil unit, a gradient coil and an MRI apparatus which can provide good linearity without reducing efficiency in generating a magnetic field.
In xe2x80x9cMethod of Manufacturing Gradient Coil, Gradient Coil unit and Gradient Coilxe2x80x9d disclosed in Japanese Patent Application Laid Open No. 6-14900, a winding pattern of a gradient coil is basically determined as follows:
(1) A winding pattern is assumed to have a plurality of bow-shaped spirals as shown in FIG. 1, and its electric current distribution in the r-direction is expressed by Eq. (2) below and that in the xcfx86-direction is expressed by Eq. (3):                                           J            r                    =                                    -                                                R                  0                                r                                      ⁢                          {                                                                    ∑                    n                                    ⁢                                                            S                      n                                        ·                                          sin                      ⁡                                              (                                                                              n                            ⁢                                                          xe2x80x83                                                        ⁢                            π                            ⁢                                                          xe2x80x83                                                        ⁢                            r                                                                                R                            0                                                                          )                                                                                            +                                                      ∑                    m                                    ⁢                                                            C                      m                                        ·                                          cos                      ⁡                                              (                                                                              2                            ⁢                            m                            ⁢                                                          xe2x80x83                                                        ⁢                            π                            ⁢                                                          xe2x80x83                                                        ⁢                            r                                                                                R                            0                                                                          )                                                                                                        }                        ⁢            sin            ⁢                          xe2x80x83                        ⁢            φ                          ,        and                            (        2        )                                                      J            φ                    =                                    {                                                -                                                            ∑                      n                                        ⁢                                                                                            S                          n                                                ·                        n                                            ⁢                                              xe2x80x83                                            ⁢                                              π                        ·                                                  cos                          ⁡                                                      (                                                                                          n                                ⁢                                                                  xe2x80x83                                                                ⁢                                π                                ⁢                                                                  xe2x80x83                                                                ⁢                                r                                                                                            R                                0                                                                                      )                                                                                                                                              +                                                      ∑                    m                                    ⁢                                                                                    C                        m                                            ·                      2                                        ⁢                    m                    ⁢                                          xe2x80x83                                        ⁢                                          π                      ·                                              sin                        ⁡                                                  (                                                                                    2                              ⁢                              m                              ⁢                                                              xe2x80x83                                                            ⁢                              π                              ⁢                                                              xe2x80x83                                                            ⁢                              r                                                                                      R                              0                                                                                )                                                                                                                                }                        ⁢            cos            ⁢                          xe2x80x83                        ⁢            φ                          ,                            (        3        )            
wherein r is a position in the radial direction, xcfx86 is a position in the angular direction, R0 is a maximum radius, and Sn, n, Cm and m are parameters to be manipulated for optimization.
(2) Optimum values for Sn, n, Cm and m are obtained at xcfx86=0. Specifically, appropriate values for Sn, n, Cm and m are assumed to calculate an linearity error of a magnetic field in a required region, and Sn, n, Cm and m are manipulated so that the linearity error falls within an allowable value, to obtain the optimum values.
(3) An electric current distribution profile on a line xcfx86=0 is obtained from Eq. (3) with the resulting Sn, n, Cm and m substituted. Ap, which is the sum of the areas of small regions enclosed by a line Jxcfx86=0 and a positive part of the electric current distribution profile from the line J101 =0, is divided by the number N of positions at which the windings of the gradient coil intersect the line xcfx86=0, and the resulting value is defined as xcex94Ap.
(4) The entire region enclosed by the line Jxcfx86=0 and the positive part of the electric current distribution profile from the line Jxcfx86=0 is separated by xcex94Ap into sub-regions. An r-position in the middle of each sub-region is defined as a position at which each of the windings intersects the line xcfx86=0.
(5) The steps (3)-(4) are repeated while sequentially varying the value of xcfx86 within a first quadrant to obtain a winding pattern in the first quadrant as shown in FIG. 2.
(6) The resulting winding pattern in the first quadrant is duplicated symmetrically with respect to the x-axis (the line xcfx86=0) to obtain a winding pattern for a fourth quadrant with the direction of electric current inverted. Moreover, a pattern for connecting the winding patterns in the first and fourth quadrants is added, considering the direction of electric current, so that one coil is formed as a whole. A winding pattern on one side is thus obtained.
(7) The winding pattern on one side is duplicated symmetrically with respect to the y-axis (an axis orthogonal to the x-axis). A winding pattern of a gradient coil unit is thus obtained.
(8) A plurality of the gradient coil units are combined.
In the conventional winding pattern of the gradient coil as above (cf. FIGS. 1 and 2), some adjacent paths carry electric current flowing in the opposite directions at some locations (in FIG. 2, at four locations).
For this reason, although good linearity can be obtained, efficiency in generating a magnetic field is reduced.
It is therefore an object of the present invention to provide a method of manufacturing a gradient coil, a gradient coil unit, a gradient coil and an MRI apparatus which can provide good linearity without reducing efficiency in generating a magnetic field.
In accordance with a first aspect of the invention, there is provided a method of manufacturing a gradient coil, comprising the steps of:
(1) assuming a winding pattern of one semicircular spiral, and expressing its x-axis electric current distribution by the following electric current distribution equation:                     J        x            ⁢              (        x        )              =                            ∑          n                ⁢                              A            n                    ·                      sin            ⁢                          (                                                π                  2                                ⁢                n                ⁢                                  x                                      R                    0                                                              )                                          +                        ∑          m                ⁢                              B            m                    ·                      sin            ⁢                          (                                                π                  2                                ⁢                m                ⁢                                  x                                      R                    0                                                              )                                            ,
wherein the x-axis is an axis dividing the semicircular spiral into two equal parts, R0 is a maximum radius, and An, n, Bm and m are parameters to be manipulated for optimization;
(2) assuming appropriate values for An, n, Bm and m so that an x-axis electric current distribution profile expressed by the electric current distribution equation with the values for An, n, Bm and m substituted does not lie in both the positive and negative polarities, calculating a linearity error of a magnetic field at a plurality of magnetic field measurement points, and manipulating An, n, Bm and m so that the linearity error falls within an allowable value, to obtain optimum values for An, n, Bm and m;
(3) dividing an area Ap of a region enclosed by the electric current distribution profile and a line Jx=0 by the number N of positions at which line members constituting a straight-line portion of the semicircular spiral intersect the x-axis, and defining the resulting value as xcex94Ap;
(4) separating the region enclosed by the electric current distribution profile and the line Jx=0 by xcex94Ap into sub-regions, and defining an x-position in the middle of each sub-region as a position at which each line member of the straight-line portion of the semicircular spiral intersects the x-axis;
(5) forming an arc-shaped portion of the semicircular spiral as a semicircle having a radius of R0, thereby generating a winding pattern on one side;
(6) symmetrically duplicating the winding pattern on one side with the respective straight-line portions adjacent to each other, thereby generating a winding pattern of a gradient coil unit; and
(7) combining a plurality of the gradient coil units.
In the method of manufacturing a gradient coil of the first aspect, a winding pattern of one semicircular spiral is assumed; its electric current distribution is expressed by a continuous function such that an x-axis electric current distribution profile does not lie in both the positive and negative polarities; parameters of the continuous function are optimized so that desired linearity can be obtained; and a position of each line member constituting a straight-line portion of the semicircular spiral is determined so that the electric current distribution profile given by the optimized continuous function is fulfilled. Then, the resulting pattern is symmetrically duplicated to generate a gradient coil unit, and a plurality of the gradient coil units are combined to form a gradient coil. This provides good linearity, and avoids reduction in efficiency in generating a magnetic field because employing a winding pattern of a semicircular spiral provides only two locations at which adjacent paths carry electric current flowing in the opposite directions, and besides the paths are well apart from each other.
In accordance with a second aspect of the invention, there is provided the method of manufacturing a gradient coil as described regarding the first aspect, wherein the plurality of magnetic field measurement points are points on a sphere that does not contain an electric current element.
In the method of manufacturing a gradient coil of the second aspect, the linearity is inspected selecting as magnetic field measurement points a plurality of points on a sphere that does not contain an electric current element, and therefore the linearity is assured also in the interior of the sphere. Thus, the calculation time can be reduced because only a small number of magnetic field measurement points on the sphere are needed for calculation.
In accordance with a third aspect of the invention, there is provided a gradient coil unit having a general structure such that a pair of winding patterns, each formed of one semicircular spiral, is symmetrically disposed with their respective straight-line portions adjacent to each other, wherein, when an axis dividing the semicircular spiral into two equal parts is defined as an x-axis, an x-axis electric current distribution generated by passing electric current through one of the semicircular spirals is basically expressed by a continuous function that does not lie in both the positive and negative polarities.
In the gradient coil unit of the third aspect, since employing a winding pattern of a semicircular spiral having an electric current distribution basically expressed by a continuous function that does not lie in both the positive and negative polarities, provides only two locations at which adjacent paths carry electric current flowing in the opposite directions, and besides the paths are well apart from each other, reduction in efficiency in generating a magnetic field can be avoided. Moreover, good linearity can be obtained by optimizing parameters of the continuous function so that desired linearity can be obtained.
In accordance with a fourth aspect of the invention, there is provided the gradient coil unit as described regarding the third aspect, wherein the continuous function consists of a combination of orthogonal functions.
In the gradient coil unit of the fourth aspect, since a continuous function consisting of a combination of orthogonal functions is employed, a calculation can be performed as separate processes, thereby making the calculation process easy.
In accordance with a fifth aspect of the invention, there is provided a gradient coil comprising a combination of a plurality of the gradient coil units as described regarding the third or fourth aspect.
In the gradient coil of the fifth aspect, since employing a winding pattern of a semicircular spiral having an electric current distribution basically expressed by a continuous function that does not lie in both the positive and negative polarities, provides only two locations at which adjacent paths carry electric current flowing in the opposite directions, and besides the paths are well apart from each other, reduction in efficiency in generating a magnetic field can be avoided. Moreover, good linearity can be obtained by optimizing parameters of the continuous function so that desired linearity can be obtained.
In accordance with a sixth aspect of the invention, there is provided an MRI apparatus comprising the gradient coil as described regarding the fifth aspect.
In the MRI apparatus of the sixth aspect, since employing a gradient coil having a winding pattern of a semicircular spiral and having an electric current distribution basically expressed by a continuous function that does not lie in both the positive and negative polarities, provides only two locations at which adjacent paths carry electric current flowing in the opposite directions, and besides the paths are well apart from each other, reduction in efficiency in generating a magnetic field can be avoided, thereby reducing electricity consumption. Moreover, since good linearity can be obtained by optimizing parameters in the continuous function so that desired linearity can be obtained, image quality can be improved.
Thus, according to the method of manufacturing a gradient coil, the gradient coil unit, the gradient coil and the MRI apparatus of the present invention, good linearity can be obtained without reducing efficiency in generating a magnetic field.
Further objects and advantages of the present invention will be apparent from the following description of the preferred embodiments of the invention as illustrated in the accompanying drawings.